The Democratic and the Republican Way to Clean the Street

Estimating Partisan Voting in Nonpartisan Offices Using Cast Vote Records

Mason Reece

MIT

May 15, 2024

Motivation

Partisanship is embedded in who we are (Campbell et al. 1960; Fiorina 1981; Green, Palmquist, and Schickler 2002) and how political parties represent themselves (Aldrich 2011)

Yet, across the U.S., 70% of local governments use nonpartisan election systems where party labels are absent from the ballot (DeSantis and Renner 1991; Svara 2003)

Question

Do patterns in vote choice also fall along a partisan divide in the absence of party labels on the ballot?

Conflicting Expectations

  1. Progressive reformers around the turn of the 20th century called for changes to insulate government from the pressure of parties and political machines (Bonneau and Hall 2009; Adrian 1952)
  2. Voters regularly rely on “heuristics,” especially in low-information elections (Downs 1957; Mondak 1993; Lau and Redlawsk 2001)

Data

One of the reasons there are conflicting expectations is that measurement of local preferences is extremely difficult (Anzia 2021)

  • Survey research is limited by sample size, question wording, survey complexity, and inaccurate reporting

  • Aggregated data must rely on strong ecological inference assumptions

I take a new approach to this problem, using ballot-level data called cast vote records (CVRs)

  • CVRs contain the true votes on all races a voter could have cast a ballot for in the election, but they only contain information on vote choice
  • I use CVRs from Adams County, Colorado

Model Estimation

Standard 2-Parameter Item-Response Theory model (Jackman 2009)

Model

\[ \begin{align*} Y_{j, k(c)} &\sim \text{Categorical}(\pi_{j, k(c)}) \\ \pi_{j, k(c)} &= \text{Pr}(y_{jk} = c | \alpha_j, \gamma_{k(c)}, \beta_{k(c)}) = \text{softmax}(\alpha_j \cdot \gamma_{k(c)} - \beta_{k(c)}) \end{align*} \]

Quantity Symbol
Individual \(j = 1, 2, …, J\)
Race \(k = 1, 2, …, K\)
Candidate \(c = 1, 2, …, C\)
Ideal point of voter \(j\) \(\alpha\)
Discrimination/Slope Parameter \(\gamma\)
Difficulty/Location Parameter \(\beta\)

Model Notes

Identification restrictions are essential Rivers (2003)

  • Normalize \(\alpha\) to mean 0, standard deviation 1

  • Let \(\gamma\) vacillate and post-process using the algorithm developed by Papastamoulis and Ntzoufras (2022)

I estimate the model under a Bayesian framework using a bespoke Stan model

Validation – Aggregated Points

Distribution of Ideal Points of Voters for Trump and Biden Voters

Validation – Geographical Distribution

Distribution of Ideal Points by State House District in Adams County, Colorado

Validation – DIME Comparison

Different latent dimensions prevent me from directly comparing estimates, instead I can only compare cutpoints

The definition of cutpoints flows from the spatial utility model for a binary choice between \(\zeta_j\) and \(\psi_j\)

\[ \begin{align*} U_i\left(\zeta_j\right) &= -\left\|\xi_i-\zeta_j\right\|^2+\eta_{i j} \\ U_i\left(\psi_j \right) &=- \left\|\xi_i-\psi_j \right\|^2+v_{i j} \end{align*} \]

where \(\xi_i \in \mathbb{R}^d\) is the ideal point of respondent \(i\) and \(\eta_{i j}\) and \(v_{i j}\) are stochastic shocks

The cutpoint is then defined as \(\frac{(\xi_j + \psi_j)}{2}\) , the point at which a respondent would find themselves indifferent between the two candidates

In the categorical model, I compute a series of pairwise comparisons between candidates

Validation – DIME Comparison

Comparison of the Cutpoints from the Categorical 2-Parameter Model and DIME Scores

Results

Results - Nonpartisan Details

Future Work

  • Sample more voters from more geographies, which is currently limited by computational cost
    • Variational inference via Pathfinder is one option
    • Machine learning prediction, akin to Bonica (2018), is another option
  • Model extensions
    • Some evidence suggests that local elections are not well-described by a single dimension (Bucchianeri 2020)
    • Include contests where voters could choose more than one candidate
  • Compare method directly with Lewis (2001) and Reece et al. (2024)
  • More than just partisanship (Anzia 2021)

References

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